Stability Improvement of the Immersed Boundary–Lattice Boltzmann Coupling Scheme by Semi-Implicit Weighting of External Force

Round 1

Reviewer 1 Report

Please see my uploaded review report.

Comments for author File: Comments.pdf

Author Response

Dear Editors and Reviewers,

We are very glad to have received so many insightful comments from you. They are very important for improving the paper. We appreciate your precise attitude towards science very much. Thanks a lot!

We have read the comments carefully and tried our best to revise it. Now we are confident that the revised version should be satisfactory.

The revision details are described in the following attachment:

Author Response File: Author Response.doc

Reviewer 2 Report

 

This paper presents a new algorithm to iteratively calculate the force exchanges between the fluid nodes and the Lagrangian nodes of an immersed boundary for flow resolved a lattice Boltzmann method. This new algorithm is an improvement on the direct iterative method that makes it much more stable and also more accurate according to the authors.

 

In spite of its poor writing, mostly because of the quality of the English that even make some parts hardly understandable, the approach is well described and the paper is relatively easy to read. The method and the objectives are clearly stated and the conclusions are supported by convincing simulations results. Beside extensive editing for the English writing, mostly minor changes are required to make it publishable. It would still be beneficial to detail the derivation of the method a little more.

 

The derivation of the method is not presented in a clear way. Only the final expression is presented in Eq. (22), but it is not clear how this is obtained by combining Cheng’s approach with the direct iteration method. The DI method should be shortly reminded in section 2, especially because it is used for comparison with the new AWI method developed by the authors, so the implementation that they have used must be presented. That would also make it more clear how this new methods derives from DI. It may even explain the name “AWI”: in the current draft, the “weighting iterative” process is not clear as no weighting functions are introduced.

 

In several places, the authors also claim that their method improves accuracy (lines 366-367 for example). While they present a convincing validation that it does not decrease accuracy (line 258), they do not provide any evidence of any improvement. They should either remove this statement (their method already has enough qualities) or provide more information supporting this conclusion.

 

The points raised in the two previous paragraphs are the most important required changes. In the following, more minor changes are detailed.

 

The authors should also proofread their draft to check the consistency of their notations. Z in Eq. (12) and Y in Eq. (13) are not defined, although Z can be inferred from the context and Y should probably just be replaced by X. Some words are missing in the sentences between lines 171 and 173, which does not help in a text that is already hard to understand. Line 201, it is not clear what U is, is it an initial velocity or a boundary condition? Where is it applied? It should be illustrated in Fig. 1. Also, the position of points N and S should be added on Fig. 1, along with the axes of directions x and y. Although in lattice units everything becomes somewhat dimensionless, it does not make much sense to compare a velocity and a displacement lines 312-313, this sentence should be reworded. With a driving velocity of 0.01 at time 8600, the filament position should be in x = 86 and the box is said to be 500×500 in the text. In Fig. 15 the filament appears very close the border, is this figure a zoom on the center of the simulation domain? Adding graduated axes would help understand most figures. The value of the viscosity of 0.1 given line 385 is most likely a typo since that would be very high viscosity for LBM, making it very unlikely to face stability issues, whatever the iterative method. Line 388, the authors state that their method improves stability, but do not state compared to which reference and this is probably true but supported by no evidence in this specific case.

 

The English quality must be improved in the text, but also in figure legends and labels. Fig. 5 reads “lagerange” for example. Beside English, there are also many typos, even in the name of the method presented in the paper, thar is “API” line 297. A careful proofreading step is required.

The English quality is very poor, but it only makes it difficult to understand in a few places since the paper is well overall organized and the main ideas are presented in a logical and clear order.

Author Response

Dear Editors and Reviewers,

We are very glad to have received so many insightful comments from you. They are very important for improving the paper. We appreciate your precise attitude towards science very much. Thanks a lot!

We have read the comments carefully and tried our best to revise it. Now we are confident that the revised version should be satisfactory.

The revision details are described in the following attachment:

Author Response File: Author Response.doc